Ductility Exhaustion Model Research Articles

Creep-fatigue life and damage evaluation under various strain waveforms for Ni-based Alloy 740H

This paper presents creep-fatigue life evaluation of a nickel-based Alloy 740H, for evaluating its performance as a material of advanced ultra-supercritical power plants. Strain controlled creep-fatigue tests were performed under six strain waveforms using solid bar specimens at 700 °C, and the effect of strain waveform on creep-fatigue life was discussed. Creep-fatigue lives were shorter than pure fatigue life depending on the strain waveform. The failure life in symmetrical waveform was reduced to about half as the strain rate decreased by one order of magnitude. The failure lives in the unsymmetrical waveforms were smaller than that in the symmetrical waveform and tensile slow straining was more detrimental to fatigue life than compressive slow straining. The creep-fatigue life decreased significantly due to strain hold, and tensile peak strain hold had more enhanced effect on fatigue life than compressive strain hold. Applicability of five existing approaches based on linear damage summation rule were discussed. In addition, a new approach based on modified ductility exhaustion model with several modifications was proposed in order to improve the life predictability of the classical approach. Time fraction rule with ASME failure envelope and new approach satisfactorily predicted the creep-fatigue lives almost within a scatter band of 2.

Numerical simulation of creep notched bar of P91 steel

Numerous components designed for use at elevated temperatures now exhibit multiaxial stress states as a result of geometric modification and material inhomogeneity. It is necessary to anticipate the creep rupture life of such components when subjected to multiaxial load. In this work finite element analysis has been performed to study the influence of different notches, namely blunt and medium notches on the stress distribution across the notch throat during the creep exposure. Within the FE model, a ductility exhaustion model based on the Cocks and Ashby model was utilized to forecast the creep rupture time of notched bar P91 material. The lower and upper bound of creep ductility are employed in the FE analysis. Different notch specimens have different stress and damage distribution. It is shown that for both types of notches, the von Mises stress is lower than the net stress, indicating the notch strengthening effect. The accumulation of creep damage in the minimum cross-section at each element across the notch throat increases over time. The point at which damage first occurs is closer to the notch root for the medium notch than for the blunt notch. The long-term rupture life predicted for blunt notch specimens appears to be comparable to that of uniaxial specimens. The upper bound creep ductility better predicts the rupture life for medium notches.

Prediction of creep crack initiation time based on constraint parameters in specimens with different geometries

Based on two creep constraint parameters (R* and Ac), the constraint-dependent creep crack initiation (CCI) time equations of a Cr–Mo–V steel at 566 °C have been established over a wide range of C* region. The equations are independent on the choice of the reference specimen. Based on the two-parameter (C*-R* and C*-Ac) and the constraint-dependent CCI time equations, the CCI time for the specimens with different geometries and dimensions (with a wide range of constraint levels) has been predicted over a wide range of C* region. The predicted CCI time agrees well with experimental data available and CCI time of finite element simulations based on the creep ductility exhaustion model. The specimen geometry with high constraint strengthens the effect of out-of-plane constraint on the CCI time. The two constraint parameters R* and Ac can give similar CCI time prediction results. The two-parameter approaches with considering constraint effect may be applied in the CCI life assessment of high-temperature components (such as pressure pipes and vessels) under static loads in operating plants.

Grain boundary sliding model for assessing creep-fatigue life of Sn37Pb eutectic solder

This study discusses the creep-fatigue life prediction of eutectic Sn37Pb solder. Creep-fatigue lives were experimentally obtained at 313 K using fast-fast, slow-slow, slow-fast, fast-slow, and strain-hold waveforms. Conventional four creep-fatigue life prediction rules, time fraction rule, strain range partitioning method, frequency modified fatigue life, and ductility exhaustion model was used to predict the creep-fatigue lives. However, not all the rules were able to properly estimate them. Since the grain boundary sliding rates were closely related to creep-fatigue lives, a new life prediction method based on grain boundary sliding rates was proposed.

An efficient fatigue and creep‐fatigue life prediction method by using the hysteresis energy density rate concept

AbstractFatigue damage, time‐dependent creep damage and their interaction are considered as the main failure mechanisms for many high temperature structural components. A generalized methodology for predicting both the high temperature low cycle fatigue (HTLCF) and creep‐fatigue lives by using the hysteresis energy density rate (HEDR) and fatigue damage stress concepts was proposed. Experimental data for HTLCF and creep‐fatigue in Alloy 617, Haynes 230 and P92 steel were respectively collected to validate the method. A better prediction capacity and most of the data points that fall within a 1.5 scatter band were obtained compared with the traditional energy‐based method, time fraction rule and ductility exhaustion model. Moreover, a creep‐fatigue damage diagram was also constructed by using the proposed approach.

Enhanced models of creep crack initiation prediction coupled the stress-regime creep properties and constraint effect

In this work, enhanced theoretical analysis and finite-element (FE) simulation were carried out to evaluate the creep crack initiation times by coupling the stress-regime creep strain rate and creep ductility and constraint effect. Firstly, the enhanced theoretical approaches were derivated based on the ductility exhaustion model, 2RN (2 regimes Norton) creep model and the Fermi's fit (between the creep ductility and creep strain rate), and several analytical models of CCI prediction were proposed under the different stress field condition. Then the constraint effect was coupled into the enhanced C*-Q* approaches. The comparison of CCI time predictions between the FE solutions and the enhanced C*-Q* approaches verified the accuracy of the latter. Reasonable and conservative predictions of CCI time could be obtained from the theoretical solutions when the constraint effects were considered in the K-RR and HRR-RR controlled models when compared with FE solutions. The K-RR and solutions were accurate when initial stress intensity factor K was at low and high range, respectively. Finally, the accuracy of the enhanced approaches and the suitability of finite element simulation were validated by the experimental data of 316H steel.

Evaluation of multiaxial creep and damage evolution for small punch creep test considering critical-strain criterion

Abstract Experiment and finite element analysis were performed in this study to estimate the deformation characteristics of small punch creep test. Considering the disadvantage of the traditional model owing to numerous unknown parameters, ductility exhaustion model was introduced and used to estimate the damage and multiaxial creep evolution process. The results show that the evolution trends of creep deflection and strain with three stages are similar. During deformation, apparent damage localization is observed. The maximum strain and damage also occurred in the necking region due to the stress concentration. Thus, a critical damage value is proposed for service-exposed Cr5Mo in this study. In the primary creep stage, a tensile deformation is observed at the lower surface and a compression deformation is observed at the upper surface. Subsequently, the stress triaxiality tends to be constant in the second creep stage. Thus, steady creep parameters of small punch test can be used to replace traditional creep results in the creep properties analysis of in-service components. Finally, the multiaxial creep and damage evolution characteristics of the small punch creep specimen are obtained.

Analytical approaches of creep crack initiation prediction coupled with the residual stress and constraint effect

Abstract In this work, the coupled effects of residual stress and constraint on creep damage and creep crack initiation time (CCI) were analyzed by the analytical approaches based on the ductility exhaustion model. The elastic follow-up factor, Z, as well as the reference stress method and constraint parameter Q* , were considered as part of the analytical method. The variation of hydrostatic stresses, triaxiality and multiaxial strain factor considering the constraint was discussed. The suitability of the analytical method to the conditions that coupled secondary stress and the constraint effects was then investigated. Reasonable and conservative predictions of CCI time could be obtained from the theoretical solutions when the coupled effects were taken into account within the Hutchinson-Rice-Rosengren--Riedel-Rice (HRR-RR) (initiation initially under the elastic-plastic Hutchinson-Rice-Rosengren (HRR) field and then under transient creep stress conditions, the Riedel-Rice (RR) controlled stress field) and stress intensity factor—Riedel–Rice (K-RR) control (initially by K, then by transient creep stress or Riedel–Rice conditions) controlled model when compared with finite element (FE) solutions. The K-RR solutions were more accurate when primary initial stress intensity factor K P I 1/2 , and the HRR-RR solutions were more appropriate when K P I >6 MPam 1/2 .

Theoretical and numerical analysis of creep crack initiation combined with primary and secondary stresses

In this work, the creep crack initiation time (CCI) considering the residual stress effects were investigated by numerical simulation and theoretical approaches based on the ductility exhaustion model. The redistribution of stress under the combined loading condition (i.e. the tensile residual stress generated by the pre-compressed loads and primary loads) was taken into account. The elastic follow-up factor, Z, as well as the reference stress method, was considered as part of the theoretical method. The suitability of the theoretical method to the conditions that included combined primary and secondary stresses was then investigated. Reasonable and conservative predictions of CCI time could be obtained from the theoretical solutions when the elastic follow-up factor, Z, was taken into account within the K-Riedel-Rice (K-RR) controlled model (initiation initially under the elastic K field and then under transient creep stress conditions, the Riedel-Rice (RR)) and the Hutchinson-Rice-Rosengren-Riedel-Rice (HRR-RR) controlled model (initiation initially under the elastic-plastic Hutchinson-Rice-Rosengren (HRR) field and then under RR controlled stress field) compared with finite element (FE) solutions. K-RR was more suitable when the primary stress intensity factor KIP was below 15 MPa m1/2, and HRR-RR was more accurate when KIP was beyond 15 MPa m1/2. However, RRss (initiation under the steady state creep) values were much higher than the FE solutions, but K (initiation under the elastic stress intensity factor K-controlled stress field) controlled values seriously underestimated the initiation times. HRR (initiation under the elastic-plastic HRR-controlled stress field) values underestimated the initiation time when load level KIP was less than 27 MPa m1/2, but slightly overestimated when KIP was larger than 27 MPa m1/2. The HRR-RR and HRR solutions were much close and may be a little unconservative at the high load levels (KIP > 27 MPa m1/2). The CCI time including the elastic follow-up factor Z was much more accurate than when ignoring the residual stress.

Prediction of creep crack initiation behavior considering constraint effects for cracked pipes

The creep crack initiation (CCI) location and time of axial surface cracks with different sizes in cracked pipes have been comparatively predicted by finite element calculations based on creep ductility exhaustion model and creep fracture mechanics considering constraint effects by using two new creep constraint parameters (R∗ and Ac). The effects of calculation methods of the parameters C∗, R∗ and Ac along the crack fronts on the prediction accuracy of CCI time have been analyzed. It has been found that with decreasing crack length, the CCI location changes from the deepest part to near surface part along the crack front, and the composite parameters composed of C∗ and constraint parameters can predict the CCI location. The CCI time of pipe cracks increases with decreasing crack depth and length due to the decrease of crack-tip constraint level. The excessive conservatism in conventional CCI life assessments using single parameter C∗ can be significantly reduced by using the two-parameter concept (C∗-R∗ and C∗-Ac) considering constraint effects. When the average values of C∗, R∗ and Ac along the crack fronts (instead of the values at the deepest locations of crack fronts) are calculated and used in CCI life predictions of cracked pipes, the prediction accuracy with respect to the finite element calculations based on creep ductility exhaustion model can be significantly improved. The C∗ values calculated by reference stress method can lead to extra conservatism in CCI life predictions.

Probabilistic fatigue life prediction and reliability assessment of a high pressure turbine disc considering load variations

In the present work, a probabilistic framework for fatigue life prediction and reliability assessment of an engine high pressure turbine disc is proposed to incorporate the effects of load variations and mean stress, which provides a reference for engine structural design under a given target failure probability. Within this framework, a new probabilistic fatigue damage accumulation model under random loadings is elaborated based on a ductility exhaustion model, and probabilistic [Formula: see text] curves for the high pressure turbine disc under different flight missions are derived based on experimental data of turbine disc alloy GH4169. The influence of random load variations on fatigue reliability of the high pressure turbine disc has been investigated and quantified by combining the engine load spectrum with finite element analysis.

Mismatch effect in creep properties on creep crack growth behavior in welded joints

The finite element method based on ductility exhaustion model was used to systematically investigate the mismatch effect in creep properties on creep crack growth (CCG) behavior in welded joints. The crack-tip damage, stress states, CCG paths, CCG rate and rupture life were calculated for different configurations of creep properties between weldment constituents under the same load level, and the creep life assessment and design for welded joints were discussed. The results show that when the zone containing the crack is softer than at least one of the other two surrounding materials or both, the creep crack propagates straight along the initial crack plane. Otherwise, it will form a second crack in the soft material near interface. These simulation results were confirmed by the experimental observations in the literature, and the mechanism was analyzed. The harder surrounding materials can lead to higher CCG rate and shorter rupture life due to the higher constraint given from them. The early initiation and propagation of the second cracks increase CCG rate and reduce rupture life, and the incubation time of the second cracks in soft materials near interfaces should be accurately determined in the creep life assessment and design for the welded joints. A proper mismatch design with harder material containing crack and softer surrounding material can improve CCG properties of welded joints (decreasing CCG rate and prolong rupture life).

Systematic Evaluation of Creep-Fatigue Life Prediction Methods for Various Alloys

Failure under creep-fatigue interaction is receiving an increasing interest due to an increased number of start-up and shut-downs in fossil power generation plants as well as development of newer nuclear power plants employing low-pressure coolant. Such situations have prompted the studies on creep-fatigue interaction and the developments of various approaches for evaluating its significance in design as well as remaining life evaluation, but most of them are fragmental and rather limited in terms of materials and test conditions covered. Therefore, applicability of the proposed approaches to different materials or even different temperatures is uncertain in many cases. The present work was conducted in order to comparably evaluate the representative approaches used in the prediction of failure life under creep-fatigue conditions as well as their modifications, by systematically applying them to available test data on a wide range of materials which have been used or are planned to be used in various types of power generation plants. The following observations have been made from this exercise: (i) The time fraction model has a tendency to be nonconservative in general, especially at low temperature and small strain ranges. Because of the large scatter of the total damage, this shortcoming would be difficult to cover by the consideration of creep-fatigue interaction in a simple manner. (ii) The classical ductility exhaustion model showed a general tendency to be overly conservative in many situations, especially at small strain ranges. (iii) The modified ductility exhaustion model based on the redefinition of creep damage showed improved predictability with a slightly nonconservative tendency. (iv) Energy-based ductility exhaustion model developed in this study seems to show the best predictability among the four procedures in an overall sense although some dependency on strain range and materials was observed.

Study of Life Prediction and Damage Mechanism for Modified 9Cr-1Mo Steel Under Creep-Fatigue Interaction

Creep-fatigue interaction is a principal cause of failures of many engineering components under high temperature and cyclic loading. In this work, stress controlled creep-fatigue interaction tests are carried out for modified 9Cr-1Mo (P91) steel. In order to study the damage mechanism of P91 steel under creep-fatigue interaction, Scanning Electron Microscopy (SEM) of specimen fracture morphology and in-situ observation experiments were conducted. Based on the ductility exhaustion theory and creep-fatigue interaction tests data, the modified ductility exhaustion life prediction model was developed. The predicted results are in a good agreement with the experiment. By comparison with frequency separation model, the life predicted by ductility exhaustion model is better than frequency separation model obviously. The results show that different stress amplitude and mean stress have great effect on the fracture damage mechanism when the hold time is invariable. By the SEM analysis of fracture morphology, the damage characters of creep, creep-fatigue interaction and fatigue can be partitioned. The specimen crack initiation source is the modified 9Cr-1Mo steel inclusion. Therefore, this work can provide a reference of life prediction and design for high temperature materials and components.

A New Ductility Exhaustion Model for High Temperature Low Cycle Fatigue Life Prediction of Turbine Disk Alloys

Based on ductility exhaustion theory and the generalized energy-based damage parameter, a new viscosity-based life prediction model is introduced to account for the mean strain/stress effects in the low cycle fatigue regime. The loading waveform parameters and cyclic hardening effects are also incorporated within this model. It is assumed that damage accrues by means of viscous flow and ductility consumption is only related to plastic strain and creep strain under high temperature low cycle fatigue conditions. In the developed model, dynamic viscosity is used to describe the flow behavior. This model provides a better prediction of Superalloy GH4133's fatigue behavior when compared to Goswami's ductility model and the generalized damage parameter. Under non-zero mean strain conditions, moreover, the proposed model provides more accurate predictions of Superalloy GH4133's fatigue behavior than that with zero mean strains.

The exhaustion of creep ductility in 1CrMoV steel

The calculation of creep damage due to secondary (self equilibrating) stresses for the lifetime assessment of critical locations in components subject to creep-fatigue loading at high temperatures may be determined in terms of ductility exhaustion. A new Spindler type stress-modified creep ductility exhaustion model has been developed for 1CrMoV steel in which the rupture ductility is dependent not only on creep strain rate, stress and temperature, but also on a material pedigree function. The paper covers the background to the development of the new model and demonstrates its capability for predicting the creep rupture ductility characteristics of heats of 1CrMoV at different positions in the alloy scatterband.

Creep-Fatigue Life Assessment for Sn-3.0Ag-0.5Cu Solder

This paper describes the creep-fatigue life assessment of Sn-3.0Ag-0.5Cu solder under pull-push loading using fast-fast, fast-slow, slow-fast and strain-hold strain waveforms. Strain controlled creep-fatigue tests were carried out using solid bar specimen, and the effect of strain waveform on the creep-fatigue life was discussed. Creep-fatigue damage was evaluated by the linear damage rule, the frequency modified fatigue life, the ductility exhaustion model, the strain range partitioning method and the grain boundary sliding model. The strain range partitioning method and the grain boundary sliding model only predicted the creep-fatigue lives within a small scatter.

R5 procedures for assessing structural integrity of components under creep and creep–fatigue conditions

The R5 high temperature assessment procedures have been developed in the UK and address both creep–fatigue crack initiation in initially defect free components and the growth of flaws by creep and creep–fatigue mechanisms. The procedures were developed some time ago and included a number of novel features such as: the shakedown reference stress approach for structural assessment; the ductility exhaustion method for estimating creep damage; the inclusion of size effects in fatigue damage calculations to enable assessments of thin section components; and the treatment of the effects of crack closure on creep–fatigue crack growth rates. Recently, the R5 procedures have undergone a major revision leading to Issue 3 of the document. In the revision, the above novel features have been retained but other parts of the procedure have been modified. These include: a restructuring of the document with associated new step-by-step procedures to enable easier application; modifications to the ductility exhaustion model to address multiaxial stresses including the triaxial stresses which may be present in regions of high welding residual stress; additional advice for assessment of weldments including fatigue strength reduction factors based on experimental data on austenitic weldments; generalised hysteresis loop construction methods for complex non-isothermal cycles, supported by laboratory data collected under non-isothermal conditions; advice on inelastic analysis when simplified shakedown methods are inapplicable; and rules for determination of interactions between creep and fatigue crack growth. The present review first describes in outline the overall structure and content of R5 Issue 3. Then the new R5 creep–fatigue crack initiation assessment procedures are set out in more detail. This includes the recent modifications and some associated background experimental and analytical work on which these modifications are based. Finally, the paper sets out the new creep–fatigue crack growth procedures in R5, again with some background information on the recent developments.

Creep-Fatigue Life Evaluation for Sn-3.5Ag Solder

This paper studies the creep-fatigue life evaluation of Sn-3.5Ag solder under push-pull loading using fast-fast, fast-slow, slow-fast, slow-slow, and strain-hold strain waves. Extensive creep-fatigue data were generated using these strain waves and the applicability of four conventional creep-fatigue damage rules, the linear damage rule, the frequency modified fatigue life, the ductility exhaustion model, and the strain range partitioning method, was examined. No conventional damage rules evaluated creep-fatigue lives accurately. Only the grain boundary sliding model, developed recently for solders, predicted creep-fatigue lives with a small scatter.

A Strain Rate Ratio Approach for Assessing Creep-Fatigue Life of 63Sn-37Pb Solder Under Shear Loading

This paper studies creep-fatigue life prediction under shear loading by making extensive torsion creep-fatigue experiments using four kinds of strain waves. The linear damage rule, strain range partitioning method, frequency modified fatigue life, and ductility exhaustion model were applied to the experimental data, but no methods accurately predicted the creep-fatigue life. A new method based on the strain rate ratio, which predicted the creep-fatigue life within a factor of 4 scatter band, was developed.